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tigry1 [53]
3 years ago
15

verify that the fucntion satisfies the three hypotheses of rolles theorem on the given interval . then find all numbers c that s

atisfy the conclusion . f(x)= x^3-2x^2-4x+2 . [ -2,2]
Mathematics
1 answer:
Ghella [55]3 years ago
4 0

The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:

<span><span>x1 </span>= 0.42801</span>

<span><span>x2 </span>= −1.51414</span>

<span><span>x3 </span>= 3.08613</span>


x1 and x2 are in the desired interval [-2, 2]

f'(x) = 3x^2 - 4x - 4

so we have:

3x^2 - 4x - 4 = 0

<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6

x_1 = -4/6 = -0.66

x_ 2 = 2

According to Rolle's theorem, we have one point in between:

x1 = 0.42801 and x2 = −1.51414

where f'(x) = 0, and that is <span>x_1 = -0.66</span>

so we see that Rolle's theorem holds in our function.

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A woman is randomly selected from the 18–24 age group. For women of this group, systolic blood pressures (in mm Hg) are normally
Naddik [55]

Answer:

X \sim N(114.8,13.1)  

Where \mu=114.8 and \sigma=13.1

We are interested on this probability

P(X>140)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

And we can find this probability using the complement rule:

P(z>1.924)=1-P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(114.8,13.1)  

Where \mu=114.8 and \sigma=13.1

We are interested on this probability

P(X>140)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:P(X>140)=P(\frac{X-\mu}{\sigma}>\frac{140-\mu}{\sigma})=P(Z>\frac{140- 1114.8}{2.6})=P(z>1.924)And we can find this probability using the complement rule:

P(z>1.924)=1-P(z

8 0
3 years ago
Y=4x+5 has a gradient of 4. What is the equation of a line parallel to it?
Setler79 [48]
It is -3,-2 is<span> Y=4x+5</span>
8 0
3 years ago
Y=2x+1
yan [13]

Answer:

(1) 2 (2) (-1/2,0) (3) (0,1)

Step-by-step explanation:

The slope of the line is the number times x. This equation is y=mx+b, where m is the slope and b is the y-intercept. In this case, m is 2, so we have our slope. The y-intercept is easy, as we already know it to be (0,1). The x-intercept is the point where the line hits x when y=0. To solve for the x-intercept, we set y to 0 and solve. We have 0=2x+1. First, we subtract 1 from both sides and get -1=2x. Next, to get x by itself, divide both sides by 2. Now we have -1/2=x. Now we have our x coordinate for our x-intercept. Because of this, we get (-1/2,0) as our x-intercept.

3 0
3 years ago
PLEASE HURRY! this is financial algebra
Zina [86]

Answer:

6 years

Step-by-step explanation:

Simple interest= P.R.T

I = $1300

P = 18000 deposit

Rate = 1.19%

T = ?

Putting into the formula we have

1300 = 18000x1.19/100xT

1300 = 18000x0.0119xT

1300 = 214.2T

Divide through to get T

T = 1300/214.2

= 6.069

So when we approximate T = 6 years

It would take 6 years to make $1300 in interest

7 0
3 years ago
Q7 Find the missing angle x
Kryger [21]

Answer:

Step-by-step explanation:

Thales theorem tells us that B is a 90

and therefore from W to o (center) is 45°

we know the total of the arc VoW is 98

180= 8x +1  + 45 +98

36 = 8x

4.5 = x

x = 4.5

7 0
3 years ago
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